Question: Simplify the following expression: $a = \dfrac{z^2 + 8z + 7}{z + 7} $
Solution: First factor the polynomial in the numerator. $ z^2 + 8z + 7 = (z + 7)(z + 1) $ So we can rewrite the expression as: $a = \dfrac{(z + 7)(z + 1)}{z + 7} $ We can divide the numerator and denominator by $(z + 7)$ on condition that $z \neq -7$ Therefore $a = z + 1; z \neq -7$